tolong jawab dengan benar dan pakai cara dan rumusnya!!!!!!.... Question from @yoschristian66

July 2022 1 10 Report

tolong jawab dengan benar dan pakai cara dan rumusnya!!!!!!

$\begin{aligned}\sf a.\ &TQ=\bf\frac{25\sqrt{3}}{2}\ cm\\\textsf{-----}&\textsf{-----------------------------------}\\\sf b.\ &PT=\bf37.5\ cm\\\textsf{-----}&\textsf{-----------------------------------}\\\sf c.\ &PR=\bf25\left(1+\sqrt{3}\right)\ cm\\\textsf{-----}&\textsf{-----------------------------------}\end{aligned}$
 

Explanation

Right-Angled Triangle (Right Triangle)

Based on the given picture, it’s known that:

QS = 25 cm
∠QSR = 45°
∠QST = 60°
∠QTP = ∠SQP = ∠RQS = 90° (right-angle)
QS is the hypothenuse of ΔQST
RS is the hypothenuse of ΔQRS
PQ is the hypothenuse of ΔPQT

Hence:

TQ = QS × sin(∠QST)
⇒ TQ = 25 × sin(60°)
⇒ TQ = 25 × ½√3
$\therefore\ \boxed{\ \bf TQ=\frac{25\sqrt{3}}{2}\ cm\ }$

PT = TQ / tan(∠QPT)
⇒ PT = TQ / tan(90°–(90°–∠SQT))
⇒ PT = TQ / tan(∠SQT)
⇒ PT = TQ / tan(90°–∠QST)
⇒ PT = TQ / tan(90°–60°)
⇒ PT = TQ / tan(30°) ∴ [ ∠QPT = 30° ]
⇒ PT = TQ × cot(30°)
⇒ PT = (25√3)/2 × cos(30°) / sin(30°)
⇒ PT = (25√3)/2 × ½√3 / ½
⇒ PT = (25√3)/2 × √3
⇒ PT = 75/2 cm
$\therefore\ \boxed{\ \bf PT=37.5\ cm\ }$

PR = PQ + QR
⇒ PR = PQ + QS [ because ∠QSR = ∠QRS = 45° ]
⇒ PR = [TQ / sin(∠QPT)] + QS
⇒ PR = [(25√3)/2 / sin(30°)] + 25
⇒ PR = [(25√3)/2 / ½)] + 25
⇒ PR = [(25√3)/2 × 2)] + 25
$\therefore\ \boxed{\ \begin{aligned}\bf PR&\bf=25+25\sqrt{3}\ cm\\&\bf=25\left(1+\sqrt{3}\right)\ cm\end{aligned}\ }$